Un Problema de Stefan Multifase con Condición Convectiva en el Borde Fijo
DOI:
https://doi.org/10.70567/mc.v42.ocsid8424Palavras-chave:
Problema de Stefan a n fases, Condición convectiva, Solución de tipo similaridad, Comportamiento asintóticoResumo
Se considera un problema unidimensional de Stefan multifase que modela los cambios de fase de un material semi-infinito, bajo una condición convectiva o de tipo Robin en el borde fijo. Se establecen condiciones suficientes sobre el parámetro que caracteriza la transferencia de calor en este borde para garantizar la existencia y unicidad de solución de tipo similaridad. En el caso en que dicho parámetro tiende a infinito, la solución de este problema converge a la del caso con condición de tipo Dirichlet en el borde fijo.
Referências
Alexiades V. y Solomon A. Mathematical modeling of melting and freezing processes. Hemisphere Publishing Corporation, Washington, 1993. https://doi.org/10.1115/1.2930032
Belhamadia Y., Cassol G., y Dubljevic S. Numerical modelling of hyperbolic phase change problems: Application to continuous casting. International Journal of Heat and Mass Transfer, 209:124042, 2023. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124042
Brosa Planella F., Please C., y Van Gorder R. Extended Stefan problem for the solidification of binary alloys in a sphere. European Journal of Applied Mathematics, 32(2):242-279, 2021. https://doi.org/10.1017/S095679252000011X
Crank J. Free and moving boundary problems. Clarendon Press, Oxford, 1984.
Dalwadi M., Waters S., Byrne H., y Hewitt I. A mathematical framework for developing freezing protocols in the cryopreservation of cells. SIAM Journal on Applied Mathematics, 80:667-689, 2020. https://doi.org/10.1137/19M1275875
Gupta S. The classical Stefan problem. Basic concepts, modelling and analysis. Elsevier, Amsterdam, 2018.
Koga S. y Krstic M. Materials Phase Change PDE Control & Estimation. Birkhäuser Springer, 2020. https://doi.org/10.1007/978-3-030-58490-0
Lunardini V. Heat transfer with freezing and thawing. Elsevier Science Publishers, Amsterdam, 1991.
Panov E. On self-similar solutions of a multi-phase Stefan problem in the half-line. Journal of Mathematical Sciences, 287:620-629, 2025. https://doi.org/10.1007/s10958-025-07627-1
Perez N. Phase Transformation in Metals. Mathematics, Theory and Practice. Springer, 2020. https://doi.org/10.1007/978-3-030-49168-0
Rubinstein L. The Stefan problem. American Mathematical Society, Providence, 1971.
Sanziel M. y Tarzia D. Neccesary and sufficient condition to obtain n phases in a onedimensional medium with a flux condition on the fixed face. Mathematicae Notae, 33:25-32, 1989.
Solomon A., Wilson D., y Alexiades V. A mushy zone model with an exact solution. Letters in Heat and Mass Transfer, 9:319-324, 1982. https://doi.org/10.1016/0094-4548(82)90040-6
Szekely J. y Themelis N. Rate phenomena in Process Metallurgy. John Wiley & Sons, Inc., 1971.
Venturato L., Cirelli M., y Tarzia D. Explicit solutions related to the Rubinstein binary-alloy solidification problem with a heat flux or a convective condition at the fixed face. Mathematical Methods in the Applied Sciences, 47:6770-6788, 2024. https://doi.org/10.1002/mma.9187
Visintin A. Models of Phase Transitions. Birkhäuser, 1996. https://doi.org/10.1007/978-1-4612-4078-5
Wilson D. Existence and uniqueness for similarity solutions of one dimensional multiphase Stefan problems. SIAM Journal on Applied Mathematics, 35:135-147, 1978. https://doi.org/10.1137/0135012
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